|INDAM Workshop on Holomorphic Iteration, Semigroups,
and Loewner Chains
Rome, 9-12 September 2008
Now, the workshop is over.
Thanks to all participants for coming!
Some pdf-files of the talks are available on this page.
The theory of iteration of holomorphic self-maps in complex manifolds has been a flourishing branch of research in Mathematics since the end of the XIX century. This area of Mathematics led to interesting and challenging problems which many mathematicians contributed to. An important feature of the theory is the variety of applications of its results to other areas such as Geometry, Operator Theory, Probability Theory, and Differential Equations.
Iteration theory deals with the dynamics of orbits of a (holomorphic) self-map of a certain (complex) space. Conjugations of different types (topological, formal, holomorphic, ...) have played a key role in this study. Nowadays, quite a lot is known about iteration theory in the unit disc but much has to be unfolded in higher dimension, especially in non-topologically trivial or non-hyperbolic domains and spaces.
A strict relative of discrete iteration is the theory of semigroups of holomorphic self-maps, or fractional iteration. This refers to the study of real-semicomplete holomorphic vector fields of complex manifolds and their associated flows and started essentially with the basic 1978 work of Berkson and Porta.
Fractional iteration is also related to Loewner's chains and their corresponding evolution families. In some particular cases, Loewner's theory can be seen as an extension of that iteration. Anyhow, the general situation seems to be unclear.
The central aspect of Loewner's theory is really a method introduced by Loewner (1923) and developed by Kufarev (1943) and Pommerenke (1965) which allows to embed the image domain of a univalent function into a continuously increasing family of domains. Since that time this method has shown to be extremely useful when dealing with many diffrerent problems, especially those having some extremal character. In fact, quite recently, Loewner's theory and some further developments have been the key to solve several long standing open problems such as the Bieberbach conjecture (De Branges, 1984) or the Mandelbroit conjecture (Lawler, Schramm and Werner, 2001).
The aim of this workshop is to bring together many international leading specialists in discrete iteration, fractional iteration, and Loewner chains as well as younger researchers interested in those topics, with the idea of presenting and discussing recent results, analyzing new techniques of proof in the area and, in general, promoting any kind of collaborations among all the participants in the meeting. Moreover, since problems in iteration theory can be tackled in different ways (geometrical, analytical, measure theory, ...), we think that having specialists with so many different backgrounds can be very useful and productive.
The workshop will be held at Istituto Nazionale di Alta Matematica (INDAM) wich is located inside the campus of Università di Roma La Sapienza.
The meeting is supported by the Istituto Nazionale di Alta Matematica (INDAM) and the ESF net Harmonic and Complex Analysis and their Applications.
The Organizing Committee